# Examples for secondary school students - page 3

1. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
2. Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
3. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
4. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
5. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
6. Transforming cuboid
Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
7. Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
8. River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
9. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
10. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
11. Rectangle
In rectangle with sides 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
12. No. of divisors
How many different divisors has number ??
13. Square and circles
Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
14. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
15. Observer
The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
16. 7 heroes
9 heroes galloping on 9 horses behind. How many ways can sort them behind?
17. Pipes
Water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flow same speed?
18. Eiffel Tower
Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?
19. Area of RT
Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
20. Ace
From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace?

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